Here's a bearing plan for Roshan's well temperament.
From A4 tune A3.
Starting with A3 we will tune the temperament from C3 to C4.
From A3 tune D3 a pure beatless fifth.
From D3 tune G3 a wide fourth beating 1.3 bps. (No one can distinguish beats to the tenth of a second, but we can try.)
From G3 tune C3 a pure beatless fifth.
From C3 tune C4.
...Test G3-C4 a pure beatless fourth.
From C4 tune F3 a narrow fifth beating 1.2 bps.
...Test C3-F3 a wide fourth also beating 1.2 bps.
Now we have FCGDA and can test the resulting M3.
...Test M3 F3-A3 to beat 6.9 bps.
From A3 tune E3 a wide fourth, to beat 1.5 bps.
...Test M3 C3-E3 to beat 5.2 bps.
From E3 tune B3 a pure beatless fifth.
...Test M3 G3-B3 to beat 7.8 bps.
From B3 tune F#3 a wide fourth, to beat 1.7 bps.
...Test M3 D3-F#3 to beat 5.8 bps.
From F#3 tune C#3 a pure beatless fourth.
...Test M3 C#3-F3 to beat 5.5 bps. Compare to D3-F#3 at 5.8 bps.
From C#3 tune G#3 a narrow fifth, beating 0.9 bps.
...Test M3 E3-G#3 to beat 6.5 bps.
From G#3 tune D#3 a pure beatless fourth.
...Test M3 D#3-G3 to beat 6.2 bps.
From D#3 tune A#3 a narrow fifth beating 1.1 bps.
...Test M3 F#3-G#3 to beat 7.3 bps.
------------------------------
Jason Kanter
Lynnwood WA
425-830-1561
------------------------------
Original Message:
Sent: 05-14-2019 13:57
From: Peter Grey
Subject: Roshan Kakiya's Well Temperament Completely Solves the Just Intonation Dilemma
I have difficulty figuring out the table but my guess is the the tempered 5ths are going to beat at roughly 2 bps...maybe slightly less. (At the 3:2 partial level...twice that at the 6:4).
Is this a reasonable estimate?
Pwg
------------------------------
Peter Grey
Stratham NH
603-686-2395
pianodoctor57@gmail.com
Original Message:
Sent: 05-14-2019 11:57
From: Roshan Kakiya
Subject: Roshan Kakiya's Well Temperament Completely Solves the Just Intonation Dilemma
Jason Kanter has produced the following charts and table for the beat rates:
http://rollingball.com/images/KakiyaWell.gif
------------------------------
Roshan Kakiya
Original Message:
Sent: 05-14-2019 11:42
From: Peter Grey
Subject: Roshan Kakiya's Well Temperament Completely Solves the Just Intonation Dilemma
So, from what I gather here it is basically:
Down a pure 4th
Up a tempered 5th
Down a pure 4th
Up a tempered 5th
Etc.
Now, can any of the math whizz's among us tell me what the approx beat speed of (at the very least) that first G-D tempered 5th would be? I can doubtlessly figure out the rest from there.
1 bps? 1.25 bps? .95 bps?... what would it be from the data presented?
On the octaves, my initial suspicion is that I would simply listen for a "sweet spot" in the midrange and then expand as needed/wanted from there. Theoretically, after establishing the temperament region, try my best to replicate it up and down with an adjustment for inharmonicity.
It's worth a try. I hate to praise or condemn until I have at least given it a fair trial. (But I do need an initial bps target).
Pwg
------------------------------
Peter Grey
Stratham NH
603-686-2395
pianodoctor57@gmail.com
Original Message:
Sent: 05-14-2019 11:18
From: Richard West
Subject: Roshan Kakiya's Well Temperament Completely Solves the Just Intonation Dilemma
Rohan said: If inharmonicity is present, the octaves should be stretched as much as is needed to make them as beatless as possible. The fifths and the fourths can be tuned in the middle octaves of the piano.
Richard replies: Okay, then. It seems like we're back to square one. Inharmonicity is present and to differing degrees from piano to piano and actually from note to note within a particular instrument. How do we define having an octave "as beatless as possible?" Totally beatless at every coincidental partial of an octave is impossible. So how do I decide how wide to make my octaves, and what are the consequences in the tuning of the intervals of the middle of the piano? How do those initial decisions get expanded to the top and bottom notes?
Richard
Original Message------
The mathematics that I have shown is based on the assumption that there is zero inharmonicity.
If inharmonicity is present, the octaves should be stretched as much as is needed to make them as beatless as possible.
The fifths and the fourths can be tuned in the middle octaves of the piano. Unisons can be tuned thereafter to completely tune the piano.
------------------------------
Roshan Kakiya
------------------------------